Control Limitations in Models of T1DM and the Robustness of Optimal Insulin Delivery

Background: In insulin therapy, the blood glucose level is constrained from below by the hypoglycemic threshold, that is, the blood glucose level must remain above this threshold. It has been shown that this constraint fundamentally limits the ability to lower the maxima of the blood glucose level predicted by many mathematical models of glucose metabolism. However, it is desirable to minimize hyperglycemia as well. Hence, a desirable insulin input is one that minimizes the maximum glucose concentration while causing it to remain above the hypoglycemic, or higher, threshold. It has been shown that this input, which we call optimal, is characterized by glucose profiles for which either each maximum of the glucose concentration is followed by a minimum or each minimum is followed by a maximum. Methods: We discuss the implication of this inherent control limitation for clinical practice and test, through simulation, the robustness of the optimal input to a number of different model and parameter uncertainties. We further develop guidelines on how to design an optimal insulin input that is robust to such uncertainties. Results: The optimal input is in general not robust to uncertainties. However, a number of strategies may be used to ensure the blood glucose level remains above the hypoglycemic threshold and the maximum blood glucose level achieved is less than that achieved by standard therapy. Conclusions: An understanding of the limitations on the controllability of the blood glucose level is important for future treatment improvements and the development of artificial pancreas systems.